Golf ball dimple profile

ABSTRACT

Golf ball dimples having a cross-sectional profile shape defined by the product of a base profile and one or more weighting functions are disclosed.

FIELD OF THE INVENTION

The present invention is directed to a golf ball dimple cross-sectional profile defined by the product of a base profile and one or more weighting functions.

BACKGROUND OF THE INVENTION

U.S. Pat. No. 4,681,323 to Alaki et al. discloses a golf ball with a plurality of recessed dimples having a shape in accordance with a certain mathematical ratio on the surface thereof.

U.S. Pat. No. 4,840,381 to Ihara et al. discloses a golf ball characterized by the shape of its dimples. The dimples have a more gentle transition over their edge portion than prior art golf balls wherein dimple edges sharply intrude into the ball surface.

U.S. Pat. No. 6,331,150 to Ogg discloses a golf ball having a surface thereon with a plurality of dimples on the surface. The contour of each of the dimples is continuous from a first edge of each of the dimples to a second opposing edge of each of the dimples.

Additional background references include, for example, U.S. Pat. No. 4,813,677 to Oka et al. and U.S. Pat. No. 4,840,381 to Ihara et al.

SUMMARY OF THE INVENTION

The present invention is generally directed to a golf ball having a plurality of recessed dimples on the surface thereof, at least a portion of which have a cross-sectional profile defined by a weighted profile. The weighted profile is the product of a base profile and at least one weighting function. In a particular embodiment, the base profile is defined by a single function. In another particular embodiment, the base profile is defined by a single continuous, differentiable function.

BRIEF DESCRIPTION OF DRAWINGS

In the accompanying drawings, which form a part of the specification and are to be read in conjunction therewith, and which are given by way of illustration only, and thus are not meant to limit the present invention:

FIG. 1 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to one embodiment of the present invention.

FIG. 2 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 3 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 4 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 5 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 6 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 7 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 8 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 9 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 10 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 11 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 12 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 13 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 14 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 15 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 16 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 17 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

FIG. 18 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention. FIG. 19 shows a dimple cross-sectional profile defined by the product of a spherical base profile and a weighting function according to another embodiment of the present invention.

DETAILED DESCRIPTION

Golf balls of the present invention include dimples having a cross-sectional shape defined by a weighted profile, the weighted profile being the product of a base dimple profile and at least one weighting function. Suitable base dimple profiles include those that can be defined by a single function, including, but not limited to, spherical, conical, catenary, elliptical, polynomial, Witch of Agnesi, frequency, Neiles parabola, and cosine profiles, and those that are defined by two or more functions, including, but not limited to, profiles comprising a top conical edge and a bottom spherical cap. Profiles comprising a top conical edge and a bottom spherical cap are further disclosed, for example, in U.S. Patent Application Publication No. 2010/0240474, the entire disclosure of which is hereby incorporated herein by reference. In a particular embodiment, the base dimple profile is defined by a single continuous, differentiable function.

One or more continuous weighting functions are applied as multiplicative constructs to the base dimple profile to produce the weighted dimple profile. For base profiles defined by a single function the weighting function(s) are applied to the entire dimple profile. For base profiles defined by two or more functions, the weighting function(s) are applied independently to one or more of the base profile functions.

Typical weighting function forms include, but are not limited to, polynomial, exponential, and trigonometric or linear combinations thereof.

In a particular embodiment, one or more continuous weighting functions are applied as multiplicative constructs to a base dimple profile defined by a single continuous, differentiable function, resulting in a continuous, differentiable weighted dimple profile.

Non-limiting examples of particularly suitable weighting functions are shown in Table 1 below.

TABLE 1 Example No. Weighting Function 1 w = 1 2 w = x 3 w = x² 4 w = x³ 5 w = x⁴ 6 w = x⁴ + x³ 7 w = x²/5 + 3x³ + x⁴ 8 w = 10x² + 3x⁴ 9 w = 3x⁴ + x³/2 + 10x 10 w = −x 11 w = −x³ 12 w = x³ − x⁴ − 2x 13 w = sin(x) 14 w = cos(x) 15 w = −x⁵ 16 w = e^(x) 17 w = −e^(x) 18 w = (−e^(2x))sin(x) 19 w = e^(2x)x³

FIGS. 1-19 show the final weighted profile defined by the product of a spherical base profile and each of weighting functions 1-19 in Table 1, respectively, with a base profile such that the golf ball diameter is 1.680 inches, the dimple diameter is 0.200 inches, and the base profile has a dimple edge angle of 14°, a chord depth of 0.0063 inches, a surface depth of 0.0122 inches, a dimple radius of 0.7953 inches, and a cap height of 0.0059 inches. The chord depth, equivalent spherical edge angle, and weighted volume ratio of the final weighted profile illustrated in each of FIGS. 1-19 is given in Table 2 below.

TABLE 2 Final Weighted Profile chord equivalent weighted FIG. Base Weighting depth spherical volume # Profile Function (inches) edge angle ratio 1 spherical w = 1 0.0126 21.08° 2.00 2 spherical w = x 0.0063 17.75° 1.53 3 spherical w = x² 0.0063 16.32° 1.33 4 spherical w = x³ 0.0063 15.57° 1.23 5 spherical w = x⁴ 0.0063 15.13° 1.17 6 spherical w = x⁴ + x³ 0.0063 15.35° 1.20 7 spherical w = x²/5 + 3x³ + x⁴ 0.0063 15.50° 1.22 8 spherical w = 10x² + 3x⁴ 0.0063 16.05° 1.29 9 spherical w = 3x⁴ + x³/2 + 0.0063 15.73° 1.25 10x 10 spherical w = −x 0.0126 17.27° 1.47 11 spherical w = −x³ 0.0126 19.45° 1.77 12 spherical w = x³ − x⁴ − 2x 0.0126 17.49° 1.50 13 spherical w = sin(x) 0.0063 18.93° 1.70 14 spherical w = cos(x) 0.0126 18.43° 1.63 15 spherical w = −x⁵ 0.0063 15.42° 1.21 16 spherical w = e^(x) 0.0063 17.04° 1.43 17 spherical w = −e^(x) 0.0126 17.98° 1.57 18 spherical w = (~e^(2x))sin(x) 0.0063 14.98° 1.15 19 spherical w = e^(2x)x³ 0.0063 15.02° 1.15

For purposes of the present disclosure, a spherical base profile is defined by the following function:

$y = {{- \sqrt{R^{2} - x^{2}}} + \sqrt{R^{2} - \left( \frac{d}{2} \right)^{2}}}$

where the origin is located along the dimple axis intersecting the chord plane at y=0, and wherein

${R = \frac{- d}{2{\cos \left( {\frac{\theta \; \pi}{180} + {a\; {\cos \left( \frac{d}{D} \right)}}} \right)}}};$

-   θ=the dimple edge angle, in degrees; -   d=the dimple diameter, in inches; and -   p=the diameter of the golf ball, in inches.

The present invention is not limited by any particular dimple pattern. Examples of suitable dimple patterns include, but are not limited to, phyllotaxis-based patterns; polyhedron-based patterns; and patterns based on multiple copies of one or more irregular domain(s) as disclosed in U.S. Pat. No 8,029,388, the entire disclosure of which is hereby incorporated herein by reference; and particularly dimple patterns suitable for packing dimples on seamless golf balls. Non-limiting examples of suitable dimple patterns are further disclosed in U.S. Pat. Nos. 7,927,234, 7,887,439, 7,503,856, 7,258,632, 7,179,178, 6,969,327, 6,702,696, 6,699,143, 6,533,684, 6,338,684, 5,842,937, 5,562,552, 5,575,477, 5,957,787, 5,249,804, 5,060,953, 4,960,283, and 4,925,193, and U.S. Patent Application Publication Nos. 2006/0025245, 2011/0021292, 2011/0165968, and 2011/0183778, the entire disclosures of which are hereby incorporated herein by reference. Non-limiting examples of seamless golf balls and methods of producing such are farther disclosed, for example, in U.S. Pat. Nos. 6,849,007 and 7,422,529, the entire disclosures of which are hereby incorporated herein by reference.

In a particular embodiment, the dimple pattern provides for overall dimple coverage of 60% or greater, or 65% or greater, or 75% or greater, or 80% or greater, or 85% or greater, or 90% or greater.

Golf balls of the present invention typically have a dimple count within a limit having a lower limit of 250 and an upper limit of 350 or 400 or 450 or 500. In a particular embodiment, the dimple count is 252 or 272 or 302 or 312 or 320 or 328 or 332 or 336 or 340 or 352 or 360 or 362 or 364 or 372 or 376 or 384 or 390 or 392 or 432.

Preferably, at least 30%, or at least 50%, or at least 60%, or at least 80%, or at least 90%, or at least 95% of the total number of dimples have a cross-sectional profile defined by the product of a base function and at least one weighting function, with the remaining dimples, if any, having a cross-sectional profile based on any known dimple profile shape including, but not limited to, parabolic curves, ellipses, spherical curves, saucer-shapes, sine curves, truncated cones, flattened trapezoids, and catenary curves. Among the dimples having a cross-sectional profile defined by the present invention, the profile of one dimple may be the same as or different from the profile of another dimple. Similarly, among the remaining dimples, if any, having a known dimple profile shape, the profile of one dimple may be the same as or different from the profile of another dimple.

The diameter of the dimples is preferably within a range having a lower limit of 0.090 inches or 0.100 inches or 0.115 inches or 0.125 inches and an upper limit of 0.185 inches or 0.200 inches or 0.225 inches.

The chord depth of the dimples is preferably within a range having a lower limit of 0.002 inches or 0.004 inches or 0.006 inches and an upper limit of 0.008 inches or 0.010 inches or 0.012 inches or 0.014 inches or 0.016 inches.

The present invention is not limited by any particular golf ball construction or any particular composition for forming the golf ball layers. For example, functionally weighted curves of the present invention can be used to form dimple profiles on one-piece, two-piece (i.e., a core and a cover), multi-layer (i.e., a core of one or more layers and a cover of one or more layers), and wound golf balls, having a variety of core structures, intermediate layers, covers, and coatings.

When numerical lower limits and numerical upper limits are set forth herein, it is contemplated that any combination of these values may be used.

All patents, publications, test procedures, and other references cited herein, including priority documents, are fully incorporated by reference to the extent such disclosure is not inconsistent with this invention and for all jurisdictions in which such incorporation is permitted.

While the illustrative embodiments of the invention have been described with particularity, it will be understood that various other modifications will be apparent to and can be readily made by those of ordinary skill in the art without departing from the spirit and scope of the invention. Accordingly, it is not intended that the scope of the claims appended hereto be limited to the examples and descriptions set forth herein, but rather that the claims be construed as encompassing all of the features of patentable novelty which reside in the present invention, including all features which would be treated as equivalents thereof by those of ordinary skill in the art to which the invention pertains. 

What is claimed is:
 1. A golf ball having a plurality of recessed dimples on the surface thereof, wherein at least a portion of the recessed dimples have a cross-sectional profile defined by a weighted profile, wherein the weighted profile is the product of a base profile and at least one weighting function, and wherein the base profile is defined by a single function.
 2. The golf ball of claim 1, wherein the base profile is selected from the group consisting of spherical, conical, catenary, elliptical, and polynomial functions.
 3. The golf ball of claim 1, wherein the base profile is selected from the group consisting of Witch of Agnesi, frequency, Neiles parabola, and trigonometric functions.
 4. The golf ball of claim 1, wherein the weighting function is selected from the group consisting of polynomial, exponential, and trigonometric functions.
 5. The golf ball of claim 1, wherein the weighted profile is the product of the base profile and a linear combination of two or more weighting functions.
 6. A golf ball having a plurality of recessed dimples on the surface thereof, wherein at least a portion of the recessed dimples have a cross-sectional profile defined by a weighted profile, wherein the weighted profile is the product of a base profile and at least one weighting function, and wherein the base profile is defined by a single continuous, differentiable function.
 7. The golf ball of claim 6, wherein the base profile is selected from the group consisting of spherical, catenary, elliptical, and polynomial functions.
 8. The golf ball of claim 6, wherein the base profile is selected from the group consisting of Witch of Agnesi, frequency, and trigonometric functions.
 9. The golf ball of claim 6, wherein the weighting function is selected from the group consisting of polynomial, exponential, and trigonometric functions.
 10. The golf ball of claim 6, wherein the weighted profile is the product of the base profile and a linear combination of two or more weighting functions.
 11. The golf ball of claim 6, wherein the weighted profile is a continuous, differentiable function. 